4D Chern-Simons theory with auxiliary fields

TL;DR

This paper introduces a 4D Chern-Simons theory with auxiliary fields that, through specific boundary conditions and deformations, reproduces the auxiliary field sigma model (AFSM), including its variants with Wess-Zumino terms, expanding the understanding of integrable sigma models.

Contribution

It establishes a novel connection between 4D Chern-Simons theory and AFSM, providing a new framework to derive and deform integrable sigma models with auxiliary fields.

Findings

Derived AFSM from 4D Chern-Simons theory with boundary conditions

Reproduced original and deformed AFSM including Wess-Zumino term

Linked twist function deformations to boundary condition modifications

Abstract

The auxiliary field sigma model (AFSM) has recently been constructed by Ferko and Smith as deformations of the principal chiral model by including auxiliary fields and the potential term given by an arbitrary univariate function. This AFSM provides an infinite family of integrable sigma models including the original $T\overline{T}$-deformation and the root $T\overline{T}$-deformation. In this paper, we propose a 4D Chern-Simons (CS) theory with auxiliary fields. Then the AFSM is derived from this CS theory with the twist function for the principal chiral model by imposing appropriate boundary conditions for the gauge field and auxiliary fields. We also derive the AFSM with the Wess-Zumino term by deforming the twist function and modifying the boundary conditions.